Fractional sublinear operators with rough kernels and their commutators on new vanishing generalized Morrey spaces

Qi Wei; Ting Mei; Qi Wei; Ting Mei

doi:10.3934/cam.2026004

Communications in Analysis and Mechanics

2026, Volume 18, Issue 1: 98-116. doi: 10.3934/cam.2026004

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Research article

Fractional sublinear operators with rough kernels and their commutators on new vanishing generalized Morrey spaces

Qi Wei ,
Ting Mei ^,

School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received: 18 December 2024 Revised: 12 October 2025 Accepted: 21 January 2026 Published: 26 January 2026
47B34, 47B38

This study focuses on a class of fractional sublinear operators, denoted as $ S_{\Omega, \alpha} $, and their commutators $ S_{\Omega, \alpha, b} $ with rough kernels. We establish the boundedness of these operators on newly emerging vanishing generalized Morrey spaces that are characterized by $ (V_\infty) $ or $ (V^*) $. The primary innovation of this paper lies in the novel approach of controlling $ S_{\Omega, \alpha} $ via the Riesz potential $ I_{\alpha} $ and the management of $ S_{\Omega, \alpha, b} $ through fractional maximal commutators with rough kernels $ M_{\Omega, \alpha-\varepsilon, b} $ and $ M_{\Omega, \alpha+\varepsilon, b} $ for some $ \varepsilon > 0 $.
- Morrey space,
- vanishing properties,
- fractional integral,
- commutators,
- rough kernel
Citation: Qi Wei, Ting Mei. Fractional sublinear operators with rough kernels and their commutators on new vanishing generalized Morrey spaces[J]. Communications in Analysis and Mechanics, 2026, 18(1): 98-116. doi: 10.3934/cam.2026004

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Abstract

This study focuses on a class of fractional sublinear operators, denoted as $ S_{\Omega, \alpha} $, and their commutators $ S_{\Omega, \alpha, b} $ with rough kernels. We establish the boundedness of these operators on newly emerging vanishing generalized Morrey spaces that are characterized by $ (V_\infty) $ or $ (V^*) $. The primary innovation of this paper lies in the novel approach of controlling $ S_{\Omega, \alpha} $ via the Riesz potential $ I_{\alpha} $ and the management of $ S_{\Omega, \alpha, b} $ through fractional maximal commutators with rough kernels $ M_{\Omega, \alpha-\varepsilon, b} $ and $ M_{\Omega, \alpha+\varepsilon, b} $ for some $ \varepsilon > 0 $.

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